Saturday, January 26, 2013

The Balance of Experience

A few months ago, a friend of mine was starting to put together a Pathfinder campaign, the Rise of the Runelords adventure path. At first, we only had the DM, myself, and one other player. (Two additional players joined later, but for awhile it was just the two.)

After the first session, he decided that, in lieu of doing math, he would just level us up whenever the adventure path said we should be a higher level. Which is entirely reasonable: not everybody DMs from a computer (and it's silly to expect a person to do the relevant math without an XP calculator).

But it got me to thinking about how there were only two of us, and how the XP system would interact with that, were it in use. (It would be a different XP system anyway, being as it was Pathfinder, but 3.5e's system is the one I know.) Now, I'm on the record as thinking the 3.5e experience system is "a work of sublime genius", and I stand by that, but I want to test it.

My thinking was this: if the XP system works (and is applied) properly, then, in an adventure path situation (where you have specific numbers of foes of specific CRs, and the number doesn't vary depending on the level of the PCs), parties containing different numbers of characters should eventually wind up having approximately the same ability to defeat foes (but not the same level). Which is to say: you should be able to run an adventure path as written for a party of any size and the challenges will (after the first few levels) wind up being appropriate to the party.

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So my test was this: pit three hypothetical parties against a hypothetical adventure path.

The first party consists of two level 1 characters. The second party consists of four level 1 characters. The third party consists of 8 level 1 characters.

The adventure path consists of groups of monsters. You're supposed to be able to beat 13 opponents of CR equal to your level before leveling up, and you're supposed to be able to beat 4 even-level encounters in a day (and you're not necessarily supposed to be able to level up without resting). So I rounded 13 down to 12, and set up this hypothetical adventure path with 76 groups of opponents: 4 groups of 3 at each CR. 4 groups of 3 CR1 monsters, 4 groups of 3 CR2 monsters, 4 groups of 3 CR3 monsters, and so on.

And then I ran the numbers. Assuming the PCs always defeat their opponents and always get precisely the correct amount of XP. Assuming the PCs get a chance to rest and level up after each encounter if they have the XP for it.

By the end of the 76 groups of opponents, the 4-person party, being the baseline around which the XP system was designed, should have just about exactly hit level 20. (Or maybe wound up a bit shy, because they faced 20 fewer opponents over the course of their career than they should have if I'd stuck to the 13-opponents-per-level rule of thumb.) But, though that happened just like it should have, that's not the point I'm going to pay attention to.

I'm going to pay attention to the point when the 2-person party dinged level 20: after the first group of CR18 foes.

At the point in the adventure when the 2-person party was dinging 20, the 4-person party was just hitting 18, and the 8-person party was just hitting 16. That's completely out of balance and needs to be fixed, right? WRONG. Absolutely, blitheringly incorrect.

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Consider this: a party of two level 20 characters has an encounter challenge rating of 22. A party of four level 18 characters has an encounter challenge rating of 22. A party of eight level 16 characters has an encounter challenge rating of 22. The system works!

(Of course, this neglects the fact that level 16 characters are a spell level or two behind level 20 characters, and it neglects the fact that the 8-person party has a massive action economy advantage. I'll assume, for the sake of perfectly spherical cows, that these two factors balance one another out.)

The first point when the encounter level of the three parties equals out is after the last group of CR6 opponents. The 2-person party is at level 8, the 4-person party is at level 6, and the 8-person party is at level 4. The three parties stay roughly on par with one another thereafter. The characters in the 2-person party wind up consistently 2 levels ahead of those in the 4-person party, and those in the 8-person party wind up consistently 2 levels behind.